Suppose money grows according to simple interest accumulation function a(t) = 1 + 0.05t. How much money would you need to invest at time 3 in order to have $3200 at time 8?

I did this:

I wanted to find out how much money was invested at time 0.

$3200 = k(1 + (0.05)(8)) which implies k = $2285.71

Then I wanted to see how much money this grew to at time 3.

x = $2285.71(1 + (0.05)(3)) which implies x = $2628.57.

So invest this amount x at time 3 in order to have $3200. Is this right based on what the question is asking? I'm not really sure. Thanks for any help in advance.